Acta mathematica scientia, Series B >
A NON-TRIVIAL PRODUCT OF FILTRATION s+ 6 IN THE STABLE HOMOTOPY ROUPS OF SPHERES
Received date: 2006-06-13
Revised date: 2007-03-05
Online published: 2009-03-20
Supported by
This research is partially supported by the National Natural Science Foundation of China (10501045, 10771105), and the NCET and the Fund of the Personnel Division of Nankai University.
By a method improving that of [1], the authors prove the existence of a nontrivial troduct of filtration, s + 6, in the stable homotopy groups of sphere, Πt−6S, which is represented up to non-zero scalar by βs+2h0(hmbn−1 −hnbm−1) ∈ Exts+6,t+sA (Zp, Zp) in the Adams spectral sequence, where p ≥ 7, n ≥ m + 2 ≥ 5, q = 2(p − 1), 0 ≤ s < p − 2, t= (s + 2+ (s + 2)p + pm + pn)q. The advantage of this method is to extend the range of s without much complicated argument as in [1].
DIAO Gao , LIU Xiu-Gui , JIN Ying-Long . A NON-TRIVIAL PRODUCT OF FILTRATION s+ 6 IN THE STABLE HOMOTOPY ROUPS OF SPHERES[J]. Acta mathematica scientia, Series B, 2009 , 29(2) : 276 -284 . DOI: 10.1016/S0252-9602(09)60028-X
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